Good lord. No no no.
First of all, for the umpteenth time, no professional historian with a doctorate specializing in the early Middle Ages (ahem) calls it "the Dark Ages" any more. That's a phrase that was coined by 18th century philosophes to condemn what they didn't like about their own society (blame the bad stuff on the "dark ages") and which gets used by book publishers and the so-called "history channel" to make money because it sounds so dramatic. Whenever you see it used, a big neon sign should go up saying "THIS PERSON HAS NO IDEA WHAT THEY'RE TALKING ABOUT."
As far as "free inquiry" goes: There was a decline in literacy and education following the breakup of the Roman Empire in its former western provinces. No doubt about that, though recent research would indicate it wasn't as catastrophic a decline as used to be made out. There was no more civilian bureaucracy, therefore a lot fewer careers requiring literacy, therefore less money for teachers and schools. How many modern college students would be there if there were no jobs waiting for them? Education continued through private tutoring in aristocratic families, who continued writing poetry and sending letters to each other, and in the Christian Church, that needed literate priests and bishops. Nobody suppressed anything, it's just that those were the "last men standing," so to speak.
It's also important, by the way, to make sure you're comparing apples to apples. How many philosophers and poets of the Roman Empire had come from Britain? None. How many from Gaul, or Spain? Maybe a couple. The intellectual powerhouses of the Roman Empire had been mostly in the East - Egypt, Greece, Asia Minor - and to a lesser extent Italy and North Africa: and those areas continued to be.
With Charlemagne's empire (768-814 and after under his heirs) you see renewed investment in basic education, opening new church schools (but also open to some non-churchmen), and the copying of books, just to make them available. With the transition from the early Middle Ages (500-1000) to the high Middle Ages (1000-1300) these schools snowball into a new intellectual/educational culture called Scholasticism. There was a new prosperity after 1000 and new opportunities in church and secular administrations for literate clerks, lawyers, and judges, so the economic incentive came back for education. Also, new texts started to become available in Latin translations of Greek classics from Arabic via Spain (long story). Philosophy, medicine, science, math, all were stimulated by the "new" ideas becoming available.
Carolingian education had been pretty basic; learn the classics and get your grammar right. Scholastics, though, realized this wasn't enough. The "authorities," Christian, Roman and Greek, didn't all agree with each other. So they had to analyze the differences and choose which to follow, or find solutions of their own. So even as they had deep reverence for ancient writers, they also developed an awareness that the ancients could be wrong, and that they could find creative new ideas to advance. As one scholastic put it, "We are like dwarfs standing on the shoulders of giants: we are lesser than they, but we see further than they did."
So far from the comic-book caricature of the Middle Ages as "dark ages" with no free inquiry and no creative thinking, the opposite was true. Education was prized, there was tremendous hunger for new books and new learning, and the whole educational system for scholastics was geared towards critical questioning of authorities and logical analysis.
Now, it is true, the high Middle Ages also saw the consolidation of a concept of "Christian society" and ever-increasing claims to authority by popes. Accusations of heresy had been rare in the early Middle Ages, and being convicted of it might mean being stripped of a church office and sent to do penance in a monastery. In the high Middle Ages, things got hairier. R.I. Moore writes of the rise of a "persecuting society." It wasn't uniquely a church thing. In both the new secular and church administrations, an ambitious man on the make could make his reputation as the guy who uncovered a heresy, much as a modern prosecutor can build a career in politics on a high-profile criminal case. Inquisitions were set up as ad hoc church courts to investigate and prosecute in areas where heresies had become widespread, and secular authorities cooperated by allowing them to operate and by executing convicted ringleaders by burning at the stake. Note that the secular authorities had to cooperate for an inquisition to happen: there never was an inquisition in England, nor, for instance, in Scandinavia, because the rulers were not interested in backing them there.
What's remarkable is how few heresy trials were brought against intellectuals for their ideas. There were a handful of burnings of a circle of intellectuals in the 11th century, Peter Abelard was made to recant some of his books in the 12th - very little else till Wycliffe and Hus in the late 14th/early 15th centuries. People were not being persecuted for "free inquiry." Rather, most inquisition victims were middle-class types who adhered to alternative religious movements that challenged church authorities. In fact, there was a very fine line between saints and heretics. Francis of Assissi bore a strong resemblance to Peter Waldes - but Francis got along with his bishop and Peter didn't. Meanwhile in the universities, different intellectuals argued very different ideas on all kinds of topics without getting dragged before the inquisition. You could pursue whatever theory you wanted in terms of astronomy or mathematics or medicine. It only got a little touchy around theology and philosophy, and even then you'd have huge debates between, say, Realists and Nominalists without anyone going to the stake for it.
Sorry for going to some length here, but this is important to me. An entire era of human history has been lampooned and demonized as "dark ages" by modern people who cannot be bothered to actually study it or understand its people. And that demonization and failure of understanding is then used ideologically to support a myth of our present that doesn't hold water.
